A Japanese slang term (ironically, first employed by otaku) used to refer to the fetish for or sexual attraction to idealized people, usually a fictional perfect young girl.

Since then, moé has come to be used as a general term for a hobby, mania or fetish (non-sexual or otherwise). This is contrasted with otaku, which would be taking the specific hobby, mania or fetish to harmful levels.

The new meaning of 'moe' is entirely caught up in issues surrounding hobbies and taste. Specifically, 'moe' means be attracted to a specific character or its specific partial element and to have a favor feeling toward it. 'Moe' suggests the condition of being infatuated with one character or thing and implies an image of someone burning with desire.
The picture becomes clearer when we hear the frequent use of 'moe' referring to specific elements or characteristics, such as 'weak girl moe,' 'young lady moe,' and 'glasses moe.' The meaning of 'glasses moe' refers to a taste that is taken with a character who wears glasses; furthermore, this taste fetishizes the feature itself of glasses-wearing. In this case, glasses are the 'moe' element.

The sex industry comparison is just an example to introduce the fetish side of the "moe" feeling. However then, why do people enjoy Anime look character to be even falling in love?

Please imagine the feeling when you first liked somebody. The passion pops up inside of your brain and heart. This is not logical and unexplainable. And "moe" is a feeling very similar to this specific moment

Moe is a personal feeling, thus you could find whatever you want moe. Generally, it describes an infatuation with a girlish kind of cuteness however. The girl doesn't necessarily have to be a child however, it can also apply to a teenager or rarely even an adult, e.g. the deredere moments of a tsundere character for example.

The word cute captures an aspect of it, but cute doesn't necessarily imply moe, while moe almost always implies cute.